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Coating

Light travelling through air is refracted when it encounters the front glass surface of a filter. Then it is refracted again when it reaches the back glass surface of that filter. Refraction means that the light ray is confronted with a change of transmission properties in the substance it is travelling through. Difficult? No. Compare it with your hand, moving through air or through water. The constitution of the water makes it much more difficult to move your hand through. With light it is something similar. But that's not all of it. On every instance of change of matter (air - glass - air) a portion of the light is reflected. The first reflection (outer) does not pass though the glass at all. It will never reach your sensor. The second reflection (inner) will reflect within the glass plane and that is called glare. This does not contribute to the overall image quality. And that is to put it mildly.
Therefore, Hoya filters are always coated. Because a coating improves the refractive, reflective and transmissive properties of a filter.

In the image you can see this effect. Both on the outer and the inner surfaces reflection occurs. A multi coating is essential to compensate for this effect. It will result in significant less glare and it improves transmission: more light passes through, since the light that is not reflected outside, will pass through and reach your sensor.
This proces of reducing refraction is rather complicated and has to do with the electro magnetic radiation that light actually is. We will not bother you with that. You only need to know that a good filter can allow up to 99,4% of the light to pass through. That is a great accomplishment.

Digital filters

Digital filters (like our own Pro1D) are not digital by nature, of course. But they were developed especially for digital photography. When digital cameras came to market, a new way of coating proved to be necessary: on the back of the filter. This is because a camera sensor, and the small inside-camera filter often attached in front of the sensor, reflect more light than an emulsion film did. The special digital filters correct any unwanted reflection from behind.